Determination of the One-to-One Correspondence between the Kinematic Screw of the Output Link and the Gradient Screw in a Singular Configuration of a Parallel Mechanism

The Gough-Stewart platform with six degrees of freedom is widely used in various mechatronic devices, for example, in measuring heads, test benches, etc. It can guarantee high accuracy in controlling the movement and orientation of the output link in the working space as well as the rigidity of the device under dynamic loads. One of the disadvantages of such mechanisms is the possible loss of controllability. A parallel mechanism of the Gough-Stewart platform type is considered. It represents the second class of singularity where the power screws translated from the kinematic chains onto the output link, become linearly dependent and reciprocal to one kinematic screw. Two singular positions of the mechanism are studied in which all points of intersection of the power screws lie on one straight line coinciding with the Ox axis of the stationary Cartesian coordinate system xOy or are arbitrarily located in the plane z = –1. The kinematic screw and the gradient screw that most rapidly exit the singularity are discussed.

References

[1] Davidson J.K., Hunt K.H. Robot and Screw Theory: Applications of Kinematics and Statics of Robotics. Oxford University Press, 2004. 467 p.

[2] Zlatanov D., Fenton R.G., Benhabib B. Singularity analysis of mechanisms and robots via a velocity-equation model of the instantaneous kinematics. Proceedings of the IEEE International Conference on Robotics and Automation, 1994, pp. 986–991.

[3] Bohigas O., Zlatanov D., Ros L., Manubens M., Porta J.M. Numerical computation of manipulator singularities. Proceedings of the IEEE International Conference on Robotics and Automation, 2012, article number 6225083, pp. 1351–1358.

[4] Glazunov V.A., Koliskor A.Sh., Krainev A.F. Prostranstvennye mekhanizmy parallel’noi struktury [Spatial mechanisms of parallel structure]. Moscow, Nauka publ., 1991. 95 p.

[5] Glazunov V.A. Struktura prostranstvennykh mekhanizmov. Gruppa vintov i strukturnye gruppy [The structure of spatial mechanisms. Group of screws and structural group]. Spravochnik. Inzhenernyi zhurnal [Handbook. An Engineering Journal]. 2010, app no. 3. pp. 1–24.

[6] Glazunov V.A., Lastochkin A.B., Shalyukhin K.A., Danilin P.O. Analysis and classification of relative manipulation devices. Journal of Machinery Manufacture and Reliability, 2009, vol. 38, no. 4, pp. 379–382.

[7] Glazunov V. Design of Decoupled Parallel Manipulators by Means of the Theory of Screws. Mechanism and Machine Theory, 2010, vol. 45, no. 2, pp. 239–250.

[8] Brio S., Arkelian V., Glazunov V.A. Usloviia peredachi dvizheniia v ploskikh manipuliatorakh parallel’noi struktury [Conditions of motion transmission in planar parallel structure manipulators]. Mashinostroenie i inzhenernoe obrazovanie [Mechanical engineering and engineering education]. 2010, no. 3, pp. 2–13.

[9] Demidov S.M., Glazunov V.A., Lastochkin V.A., Artemenko Y.N. Analysis of pressure angles and special positions of parallel structure modules intended for mechanisms of relative manipulation. Journal of Machinery Manufacture and Reliability, 2011, vol. 40, no. 5, pp. 415–422.

[10] Merlet J.P. Parallel robots. Springer Science & Business Media, 2001. 178 p.

[11] Merlet J.P. A formal-numerical approach for robust in workspace singularity detection. IEEE Transactions on Robotics, 2007, vol. 23, is. 3, pp. 393–402.

[12] Gosselin C., Angeles J. Singularly analysis of closed loop kinematic chains. IEEE Transactions on Robotics and Automation, 1990, vol. 6, is. 3, pp. 281–290.

[13] Jiang Q.M., Gosselin C.M. Determination of the maximal singularity-free orientation workspace for the Gough–Stewart platform. Mechanism and Machine Theory, 2009, vol. 44, no. 6, pp. 1281–1293.

[14] Pickard J.K., Carretero J.A. An interval analysis method for wrench workspace determination of parallel manipulator architectures. CCToMM Mechanism, Machines, and Mechatronics (M3) Symposium, 2015. Available at: http://www.cctomm.mae.carleton.ca/CCToMM_2015.pdf (accessed 15 March 2017).

[15] Rui Zeng, Shuling Dai, Wenfang Xie, Xiaoming Zhand. Determination of the Proper Motion Range for the Rotary Actuators of 6-RSS Parallel Robot. CCToMM Mechanism, Machines, and Mechatronics (M3) Symposium, 2015. Available at: http://www.cctomm.mae.carleton.ca/CCToMM_2015.pdf (accessed 15 March 2017).